Context. The Parker Solar Probe and the incoming Solar Orbiter mission will provide measurements of solar energetic particle (SEP) events at close heliocentric distances from the Sun. Up to present, the largest data set of SEP events in the inner heliosphere are the observations by the two Helios spacecraft. Aims. We re-visit a sample of 15 solar relativistic electron events measured by the Helios mission with the goal of better characterising the injection histories of solar energetic particles and their interplanetary transport conditions at heliocentric distances <1 AU. Methods. The measurements provided by the E6 instrument on board Helios provide us with the electron directional distributions in eight different sectors that we use to infer the detailed evolution of the electron pitch-angle distributions. The results of a Monte Carlo interplanetary transport model, combined with a full inversion procedure, were used to fit the observed directional intensities in the 300–800 keV nominal energy channel. Unlike previous studies, we have considered both the energy and angular responses of the detector. This method allowed us to infer the electron release time profile at the source and determine the electron interplanetary transport conditions. Results. We discuss the duration of the release time profiles and the values of the radial mean free path, and compare them with the values reported previously in the literature using earlier approaches. Five of the events show short injection histories (<30 min) at the Sun and ten events show long-lasting (>30 min) injections. The values of mean free path range from 0.02 AU to 0.27 AU. Conclusions. The inferred injection histories match with the radio and soft X-ray emissions found in literature. We find no dependence of the radial mean free path on the radial distance. In addition, we find no apparent relation between the strength of interplanetary scattering and the size of the solar particle release.